But all acknowledge that it is a development of major significance for their island.
The independent, Greek-language Nicosia Politis quotes Greek politicians as saying "that the Cyprus solution can be accepted only if it leads to a confederal state with one sovereignty, one nationality, one international personality".
O Filelevtheros, a Greek independent daily, says "the Annan plan contains both positive and negative points... With the submission of the plan yesterday the governments of the United States and Britain started putting pressure for its acceptance."
The paper's editorial says "we have nothing to fear from the plan for a Cyprus solution, a plan we should face on the basis of a strategy and not emotionally."
The English-language independent Cyprus Mail says "one thing is certain about the Cyprus plan", and that is that neither side "will get what it wants."
The paper notes that "nobody, apart from the small clique of hard-line morning radio show guests, could have expected a document cut to the measures of the Greek Cypriot side."
Alithia, a rightist Greek daily, says that the plan is "a historic development".
Its editorial refers approvingly to the plan to hold a referendum, saying: "The last say for the acceptance or rejection of the result of the negotiations belongs to the people of Cyprus".
Nightmare solution
But I Simerini, a Greek-language, right-of-centre paper, calls the Annan proposal a "nightmarish solution plan".
"Athens and Nicosia will find themselves before nightmarish dilemmas next month... These dilemmas concern the fate of the Republic of Cyprus, the viability of the solution, and the legislation of the faits accomplis of the invasion," it says.
"The die has been cast... the fate of Cyprus is now in the balance."
Territorial concessions
The Turkish Cypriot newspaper Nicosia Kibris quotes Turkish Cypriot leader Rauf Denktas saying that the plan could result in an agreement, if bargaining is allowed.
The Nicosia Volkannotes that the plan calls for a considerable territorial concessions.
The paper publishes a map on its front page, and says the proposal provides for the evacuation of some 80 Turkish villages.
A columnist in the same paper asks "Is this a UN plan or a Greek Cypriot plan?"
Nicosia Afrika, a protest name assumed by former centre-left opposition paper Avrupa, is critical of Denktas' administration and Turkey.
It carries the headline "Plan is new, Denktas is old."
The paper argues that Denktas' initial reaction has been negative, sending the message that Cyprus' EU membership should be put on hold.
The paper says it wants Cyprus to join the EU soon, as a united island.
BBC Monitoring, based in Caversham in southern England, selects and translates information from radio, television, press, news agencies and the Internet from 150 countries in more than 70 languages.